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具饱和传染率的一类捕食者-食饵模型的分析 被引量:5

Analysis of a Predatro-Prey Model With a Saturated Infection Rate
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摘要 讨论了疾病仅在食饵中传播的捕食者-食饵模型.假设捕食者只捕食染病的食饵种群,且疾病的发生率为非线性的.本文首先讨论系统解的有界性,然后讨论系统平衡点的存在性及其存在时的稳定性,得到了边界平衡点和正平衡点的全局稳定性. In this paper,we study the predator-prey model with disease in the prey. Assume that the predator eats only the infected prey, and the incidence rate of disease is saturated. First of all, we study the boundedness of solutions,then we discuss the existence of equilibrium and its stability, and obtain the global stabilities of boundary equilibrium and positive equilibrium.
作者 幸玲 刘宣亮
出处 《南京师大学报(自然科学版)》 CAS CSCD 北大核心 2011年第3期25-31,共7页 Journal of Nanjing Normal University(Natural Science Edition)
基金 国家自然科学基金(10871074)
关键词 捕食者-食饵模型 有界性 中心流形 稳定性 predator-prey model, boundedness, center manifold, stability
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参考文献12

  • 1Chattopadhyay J, Arino O. A predator-prey model with disease in the prey [ J ]. Nonlinear Analysis, 1999, 36 (6) : 747-766. 被引量:1
  • 2Xiao Y, Chen L. Analysis of a three species eco-epidemiological model [ J ]. Journal of Mathematical Analysis and Applica- tions, 2001,258(2) : 733-754. 被引量:1
  • 3Xiao Yanli, Chen Lansun. A ratio-dependent predator-prey model with disease in the prey [ J ]. Applied Mathematics and Computation, 2002,131 (2) : 397-414. 被引量:1
  • 4Hethcote H W, Wang W, Han L, et al. A predator-prey model with infected prey [ J ]. Theoretical Population Biology, 2004, 66(3) : 259-268. 被引量:1
  • 5Regoes R R, Ebert D, Bonhoeffer A. Dose-dependent infection rates of parasites produce the Allee effect in epidemiology [ J ]. Proc Roy Soc Lond, 2002,269(1 488) : 271-279. 被引量:1
  • 6Li Guihua, Wang Wendi. Bifurcation analysis of an epidemic model with nonlinear incidence [ J ]. Applied Mathematics and Computation, 2009,214(2) : 411-423. 被引量:1
  • 7Liu W M, Levin S A, Iwasa Y L. Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models [J]. Math Biol, 1986,23(2) : 187-204. 被引量:1
  • 8徐为坚.具有种群Logistic增长及饱和传染率的SIS模型的稳定性和Hopf分支[J].数学物理学报(A辑),2008,28(3):578-584. 被引量:18
  • 9Ruan Shigui, Wang Wendi. Dynamical behavior of an epidemic model with a nonlinear incidence rate [ J ]. Differential Equations, 2003,188(1) : 135-163. 被引量:1
  • 10贺昱曜,闫茂德编著..非线性控制理论及应用[M].西安:西安电子科技大学出版社,2007:308.

二级参考文献10

  • 1宋新宇,肖燕妮,陈兰荪.具有时滞的生态-流行病模型的稳定性和Hopf分支[J].数学物理学报(A辑),2005,25(1):57-66. 被引量:27
  • 2原三领,马知恩,韩茂安.一类含时滞SIS流行病模型的全局稳定性[J].数学物理学报(A辑),2005,25(3):349-356. 被引量:13
  • 3Kermack W O, McKendrick A G. Contribution to the mathematical theory of epidemics. Proc Roy Soc, 1932, 138(1): 55-83 被引量:1
  • 4Cooke K L, York J A. Some equations modeling growth processes and gonorrhea epidemics. Math Biol, 1973, 16(1): 75-101 被引量:1
  • 5Busenberg S, Cooke K L. The effect of integral conditions in certain equations modeling epidemics and DoDulation growth. J Math Biol, 1980, 10(1): 13-32 被引量:1
  • 6Li J, Ma Z. Qualitative analysis of SIS epidemic model with vaccination and varying total population size. Mathl Comput Modelling, 2002, 35:1235-1243 被引量:1
  • 7Li Jianquan, Ma Zhien, Zhou Yicang. Glbal analysis of sis epidemic model with a simple vaccination and multiple endemic equilibria. Acta Mathematica Scientia, 2006, 26B(1): 83-93 被引量:1
  • 8Cooke K L, van den Driessche P, Zou X. Interaction of maturation delay and nonlinear birth in population and epidemic models. J Math Biol, 1999, 39(2): 332-352 被引量:1
  • 9Anderson R M, May R M. Population biology of infectius diseases I. Nature, 1979, 280(5721): 361-367 被引量:1
  • 10Dietz K. Overall Population Patterns in the Transmission Cycle of Infection Disease Agents. In: Anderson R M, May R M. Population Biology of Infectious Diasease. Berlin: Springer, 1982. 87-102 被引量:1

共引文献45

同被引文献15

  • 1孙树林,原存德.捕食者具有流行病的捕食-被捕食(SI)模型的分析[J].生物数学学报,2006,21(1):97-104. 被引量:51
  • 2Chattopadhyay J, Arino O. A predator-prey model with disease in the prey [ J ]. Nonlinear Analysis, 1999,36 (6) :747-766. 被引量:1
  • 3Xiao Y,Chen L. Analysis of a three species eco-epidemiological model[ J]. Journal of Mathematical Analysis and Applications, 2001,258(2) :733-754. 被引量:1
  • 4Liu X L. Bifurcation of an eco-epidemiological model with a nonlinear incidence rate [ J ]. Applied Mathematics and Computation, 2011 ,218 ( 5 ) : 2300-2309. 被引量:1
  • 5Sasmal K M, Chattopadhyay J. An eco-epidemiological system with infected prey and predator subject to the weak Allee effect [ J ]. Mathematical Biosciences,2013,246(2) :260-271. 被引量:1
  • 6Bate A M, Hilker F M. Complex dynamics in an eco-epidemiological model[ J ]. Bull Math Biol,2013,75 (11 ) :2059-2078. 被引量:1
  • 7Carrillo F, Verduzco F. Analysis of the Takens-Bogdanov bifurcation on m-parameterized vector fields [ J ]. International Journal of Bifurcation and Chaos,2010,20(4) :995-1005. 被引量:1
  • 8Kuznetsov Y. Elements of applied bifurcation theory [ M ]. New York:Springer, 1998. 被引量:1
  • 9赵丽萍,李自珍,王文婷,马智慧.一类疾病垂直感染的生态-流行病模型的动力学研究[J].兰州大学学报(自然科学版),2009,45(4):127-132. 被引量:11
  • 10王淑璠,马智慧,李文龙,李自珍.具有庇护所效应的生态流行病模型[J].兰州大学学报(自然科学版),2013,49(5):703-708. 被引量:8

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